At 01:33 PM 12/26/2007, you wrote:
Well, sure. But the [random] poisson_distribution function doesn't return the normal at high means. It returns 0 (slowly!). That's just wrong. It should either be fixed or throw an exception.
. . .
How far off is the Poisson distribution from the normal at a mean of 750? How large a sample would you need to have, say, a one in a thousand chance of detecting the difference? (I don't know the answer, but if there is a problem at that extreme, its a question that should be answered before getting too fancy with "precise" solutions).
Topher
I was implying (when I should have been saying) that at some point the error of generating a *normal* random variant with a mean and standard deviate of lambda instead of a "for real" Poisson becomes too small to have any practical significance. If large lambdas are causing problems then one solution is to see if this is only occurring sufficiently far into that regime then it might make sense to just generate a normal instead. Scaling and shifting by 750 is not likely to cause much rounding errors for a standard normal deviate, but many direct algorithms for that extreme a value are likely to run into numerical problems. Topher